nrow=16;
ncol = 24;
lambda = matrix(sample.int(100, size = ncol*nrow, replace = T),nrow,ncol);
lambda = lambda - diag(lambda)*diag(x=1, nrow, ncol);
y = rpois(ncol,lambda) + rtruncnorm(ncol,0,1,mean = 0, sd = 1);

x = matrix (0, nrow, 1);
x_A1 = y[1]+y[2]+y[3];
x_A2 = y[4]+y[7]+y[3];
x_B1 = y[4]+y[5]+y[6];
x_B2 = y[11]+y[1];
x_C1 = y[7]+y[8]+y[9];
x_C2 = y[2]+y[5]+y[12];
x_D1 = y[10]+y[11]+y[12];
x_D2 = y[3]+y[6]+y[9];
x_E1 = y[13]+y[14]+y[15];
x_E2 = y[18]+y[19]+y[23];
x_F1 = y[20]+y[21]+y[19];
x_F2 = y[22]+y[16]+y[13];
x_G1 = y[23]+y[22]+y[24];
x_G2 = y[14]+y[17]+y[20];
x_H1 = y[16]+y[17]+y[18];
x_H2 = y[15]+y[21]+y[24];

d <- c(x_A1, x_A2,x_B1, x_B2,x_C1, x_C2,x_D1, x_D2,x_E1,
       x_E2,x_F1, x_F2,x_G1, x_G2,x_H1, x_H2)
x <- matrix(d, nrow, byrow=TRUE)

A = matrix(c(1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_A^1
             0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_A^2
             0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_B^1
             1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_B^2
             0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_C^1
             0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, #x_C^2
             0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0, #x_D^1
             0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, #x_D^2
             0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0, #x_E^1
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0, #x_E^2
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0, #x_F^1
             0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0, #x_F^2
             0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0, #x_G^2
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1, #x_G^1
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0, #x_H^1
             0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1), #x_H^2
           nrow, ncol, byrow= TRUE)

eval_f <- function( yhat ) {
  return( list( "objective" = norm((mean(yhat-y))^2, type = "2")))
}

# inequality constraint
eval_g_ineq <- function( yhat ) {
  constr <- c(0 - yhat)
  return( list( "constraints"=constr ))
}

# equalities constraint
eval_g_eq <- function( yhat ) {
  constr <- c( x-A%*%yhat )
  return( list( "constraints"=constr ))
}

x0 <- y

#lower bound of control variable
lb <- c(matrix (0, ncol, 1))

local_opts <- list( "algorithm" = "NLOPT_LD_MMA",
                    "xtol_rel" = 1.0e-7 )
opts <- list( "algorithm" = "NLOPT_LD_AUGLAG",
              "xtol_rel" = 1.0e-7,
              "maxeval" = 1000,
              "local_opts" = local_opts )
res <- nloptr( x0=x0,
               eval_f=eval_f,
               eval_grad_f = NULL,
               lb=lb,
               eval_g_ineq = eval_g_ineq,
               eval_g_eq=eval_g_eq,
               opts=opts)
print(res)

**#model <- list()
#model$B <- A
#model$obj <- norm((y-yhat)^2, type = "2")
#model$modelsense <- "min"
#model$rhs <- c(x,0)
#model$sense <- c('=', '>=')
#model$vtype <- 'C'
#result <- gurobi(model, params)
#print('Solution:')
#print(result$objval)
#print(result$yhat)**